Question

A certain supernova remnant in our galaxy is an expanding spherical shell of glow-ing gas. The angular diameter of the remnant, as seen from Earth, is 22.0 arcsec. The parallax of the remnant is known to be 4.17 mas from space telescope measurements.Compute its distance in parsecs and radius in astronomical units.

Answer 1

Firstable, some definitions so you can understand better what have you been asked.

Parallax is a displacement or difference in the apparent position of an object viewed along two different lines of sight, and is measured by the angle or semi-angle of inclination between those two lines. You can relate this quantity with the distance between supernova and Earth by this equation:

The parallax is given in mas, so you have to convert it to arcsec, that's the reason of 0.001 in the equation. This distance D, is given in parsec.

Angular Diameter describes how large a sphere or circle appears from a given point of view. You need to know, angular diameter, and D (distance) and apparent size (diameter, d) to get the radius. In this case, it's better to use radius (r): diameter/2:

d= 2r = D tan(angular diameter) ==> r = (D/2) tan(angular diameter)

Be careful with units, so with angular diameter which have arcsec units must be changed to grades. 1 arcsec = 0.0003 grades.

Finally, the units of r are in parsec so convert units to UA. 1 parsec = 206265 UA.

Hopefully this will help you to get the correct answer.